1. Field of the Invention
This invention relates to an optical wavelength converting apparatus for converting a fundamental wave into its second harmonic. This invention particularly relates to an optical wavelength converting apparatus, wherein a crystal of a nonlinear optical material, with which the type II of phase matching between a fundamental wave and its second harmonic is effected, is utilized.
2. Description of the Prior Art
Various attempts have heretofore been made to convert the fundamental wave of a laser beam into its second harmonic, e.g. to shorten the wavelength of a laser beam, by using a nonlinear optical material. As an optical wavelength converting apparatus for carrying out such wavelength conversion, there has heretofore been known a bulk crystal type of optical wavelength converting apparatus as described in, for example, "Hikari Electronics No Kiso" (Fundamentals of Optoelectronics) by A. Yariv, translated by Kunio Tada and Takeshi Kamiya, Maruzen K.K., pp. 200-204.
Also, laser diode pumped solid lasers have been proposed in, for example, Japanese Unexamined Patent Publication No. 62(1987)-189783. The proposed laser diode pumped solid lasers comprise a solid laser rod, which has been doped with a rare earth metal, such as neodymium (Nd). The solid laser rod is pumped by a semiconductor laser (a laser diode). In the laser diode pumped solid laser of this type, in order for a laser beam having as short a wavelength as possible to be obtained, a bulk single crystal of a nonlinear optical material for converting the wavelength of a laser beam, which has been produced by solid laser oscillation, is located in a resonator of the solid laser. The laser beam, which has been produced by the solid laser oscillation, is thereby converted into its second harmonic, or the like.
As the crystal of the nonlinear optical material, a biaxial crystal, such as a KTP crystal, is often employed. How to effect the phase matching with a KTP biaxial crystal is described in detail by Yao, et al. in J. Appl. Phys., Vol. 55, p. 65, 1984. The method for effecting the phase matching with a biaxial crystal will be described hereinbelow.
With reference to FIG. 4, the direction, along which a fundamental wave travels, and the optic axis Z of the crystal make an angle .theta.. The projection of the direction, along which the fundamental wave travels onto the plane in which the optic axes X and Y lie, and the optic axis X make an angle .o slashed.. The refractive index of the crystal with respect to the fundamental wave, which impinges upon the crystal at an arbitrary angle of incidence, and the refractive index of the crystal with respect to the second harmonic of the fundamental wave are represented respectively by EQU n.sup..omega., n.sup.2.omega. ( 1)
The refractive indexes of the crystal with respect to the light components of the fundamental wave, which have been polarized respectively in the X, Y, and Z optic axis directions, and the refractive indexes of the crystal with respect to the light components of the second harmonic, which have been polarized respectively in the X, Y, and Z optic axis directions, are represented by ##EQU1##
When k.sub.X, k.sub.Y, and k.sub.Z, are defined as follows: EQU k.sub.X =sin .theta..multidot.cos .o slashed. EQU k.sub.Y =sin .theta..multidot.sin .o slashed. EQU k.sub.Z =cos .theta.
the following formulas obtain: ##EQU2##
Solutions of Formulas (3) and (4) represent the conditions under which the phase matching can be effected.
When B1, C1, B2, and C2 are defined as follows: ##EQU3## the solutions of Formulas (3) and (4) are represented by the formulas ##EQU4## When the condition EQU n.sup..omega.,.sub.2 =n.sup.2.omega.,.sub.1 ( 8)
is satisfied, the phase matching between the fundamental wave and its second harmonic is effected. Such phase matching is referred to as the type I of phase matching.
Also, when the condition EQU 1/2(n.sup..omega.,.sub.1 +n.sup.2.omega.,.sub.2)=n.sup..omega.,.sub.1( 9)
is satisfied, the phase matching between the fundamental wave and its second harmonic is effected. Such phase matching is referred to as the type II of phase matching.
In cases where the type II of phase matching is effected with a biaxial crystal, the fundamental wave impinging upon the crystal is subjected to two refractive indexes of the crystal. By way of example, the nonlinear optical constant d24 of the crystal may be utilized. Specifically, as illustrated in FIG. 5, a fundamental wave 11, which has been polarized linearly in the direction indicated by the double headed arrow P, may be introduced into a crystal 10. The direction indicated by the double headed arrow P inclines at an angle of 45.degree. from the Y optic axis of the crystal 10 towards the Z axis of the crystal 10. (The fundamental wave 11 comprises the linearly polarized light component in the Y axis direction and the linearly polarized light component in the Z axis direction.) In this manner, a second harmonic 12, which has been polarized linearly in the Y axis direction, may be obtained from the crystal 10. In such cases, the linearly polarized light component of the fundamental wave 11 in the Z axis direction is subjected to a refractive index EQU n.sup..omega.,.sub.1 ( 10)
Also, the linearly polarized light component of the fundamental wave 11 in the Y' direction, which direction is normal to the direction of travel of the fundamental wave 11 and to the Z axis, is subjected to a refractive index EQU n.sup..omega.,.sub.2 ( 11)
Thus the fundamental wave 11 is subjected to the two refractive indexes.
Strictly speaking, in cases where the crystal 10 has been cut into the shape shown in FIG. 5, the fundamental wave 11 impinges upon the crystal 10 such that it has been polarized linearly in the Y' direction (which inclines from the Y axis towards the X axis) and in the Z axis direction. The second harmonic 12 is obtained as light which has been polarized in the Y' direction. However, practically, no problem occurs when consideration is made in the manner described above.
As described above, in cases where the type II of phase matching is to be effected with a biaxial crystal, a fundamental wave, which has been polarized linearly in one direction, has heretofore impinged upon a nonlinear optical material such that polarized light components may occur in directions along which the two crystallographic axes of the nonlinear optical material extend. Therefore, the fundamental wave has heretofore been subjected to two refractive indexes. If the fundamental wave is subjected to two refractive indexes, a phase difference .DELTA. will occur between the polarized light components, which are subjected to different refractive indexes. The phase difference A is represented by the formula EQU .DELTA.=(n.sup..omega.,.sub.2 -n.sup..omega.,.sub.1)L.multidot.2 .pi./.lambda. (12)
where .lambda. represents the wavelength of the fundamental wave, and L represents the length of the crystal. The length, L, of the crystal is the effective length, i.e., the length of the optical path of the fundamental wave in the crystal.
If the phase difference .DELTA. occurs, the direction of linear polarization of the fundamental wave will change in accordance with the value of the phase difference .DELTA.. If the direction of linear polarization of the fundamental wave thus changes, the angles of the direction of linear polarization of the fundamental wave, with respect to the optic axes of the crystal of the nonlinear optical material, will shift from the predetermined values of the angles, at which the maximum possible efficiency of wavelength conversion can be achieved. As a result, the output power of the second harmonic becomes low. Such fluctuations in the output power of the second harmonic occur periodically. The fluctuations in the output power of the second harmonic are classified into those which are dependent on the temperature and which occur in the pattern shown in FIG. 6, in accordance with the dependency of the parameters in Formula (12) upon the temperature, and those which are dependent on the length of the crystal and which occur in the pattern shown in FIG. 7.
Therefore, in order for the second harmonic having the maximum possible output power to be obtained, it is necessary that the temperature of the crystal or the length of the crystal be set to appropriate values. An example of an optical wavelength converting apparatus, in which the temperature of a crystal is adjusted, is disclosed in, for example, U.S. Pat. No. 4,913,533. Also, examples of optical wavelength converting apparatuses, in which the length of a crystal is adjusted, are disclosed in, for example, Japanese Unexamined Patent Publication Nos. 1(1989)-152781 and 1(1989)-152782.
Also, in Japanese Unexamined Patent Publication No. 1(1989)-152781, an optical wavelength converting apparatus is disclosed in which a crystal of a nonlinear optical material having a trapezoidal cross-sectional shape is located in a resonator. The crystal is moved up and down with respect to the trapezoid, and the length of the optical path of the fundamental wave in the crystal is thereby changed. In this manner, the phase difference .DELTA. is adjusted.
However, in cases where the length of the crystal is kept the same, and the temperature of the crystal is adjusted such that the second harmonic having the maximum possible output power may be obtained, a large electric power source for the adjustment of the temperature and a large heat sink must be employed such that the temperature of the crystal may be adjusted to a value falling within a wide range. Therefore, the size of the optical wavelength converting apparatus cannot be kept small in size, and the cost of the optical wavelength converting apparatus cannot be kept low.
Also, ordinarily, in cases where the temperature of the crystal is adjusted to a predetermined appropriate value, it inevitably occurs that the position, at which the temperature of the crystal is monitored, (or the position at which the temperature in the resonator is monitored) and the part of the crystal, through which the fundamental wave actually passes, are spaced apart from each other. Therefore, if the temperature in the optical wavelength converting apparatus is changed by a change in the ambient temperature, or the like, the detected temperature will not coincide with the temperature of the part of the crystal, through which the fundamental wave passes. As a result, the temperature of the part of the crystal through which the fundamental wave passes will be adjusted to a value different from the desired value. Accordingly, the second harmonic having the maximum possible output power cannot be obtained.
In cases where the temperature of the crystal is kept the same, and the length of the crystal is adjusted to a value appropriate for the temperature of the crystal, the length of the crystal must be adjusted very strictly. Therefore, it is difficult for the second harmonic having the maximum possible output power to be obtained. Even if it is possible for the second harmonic having the maximum possible output power to be obtained, because the length of the crystal must be measured and adjusted strictly, the cost of the optical wavelength converting apparatus cannot be kept low.
With the optical wavelength converting apparatus disclosed in Japanese Unexamined Patent Publication No. 1(1989)-152781, it is necessary for the crystal of the nonlinear optical material to be moved a comparatively large distance. Therefore, if the direction of linear polarization of the fundamental wave is adjusted, the position of the resonator mode will shift from the correct position. Also, with the optical wavelength converting apparatus disclosed in Japanese Unexamined Patent Publication No. 1(1989)-152781, the fundamental wave easily undergoes the longitudinal multimode. As a result, the problem occurs in that mode competition noise occurs easily.